Given that a = 5 + 2√6 and b = 1, we need to find the true value of a² + b².
First, let's calculate a²:
a = 5 + 2√6
a² = (5 + 2√6)²
Expanding the square of a binomial:
a² = 25 + 20√6 + 24
a² = 49 + 20√6
Next, let's calculate b²:
b = 1
b² = 1²
b² = 1
Now, we can find the sum of a² + b²:
a² + b² = 49 + 20√6 + 1
a² + b² = 50 + 20√6
Therefore, the true value of a² + b² is 50 + 20√6.
